$D_s^{+}\to \varphi {\rho }^{+}$ Decay

Abstract

Motivated by the experimental measurement of the decay rate, $\Gamma$, and the longitudinal polarization, $P_L$, in the Cabibbo favored decay $D_s^{+}\to \varphi {\rho }^{+}$, we have studied theoretical prediction within the context of factorization approximation invoking several form factors models. We were able to obtain agreement with experiment for both $\Gamma$ and $P_L$ by using experimentally measured values of the form factors $A_1^{D_s\varphi }(0)$, $A_2^{D_s\varphi }(0)$ and $V^{D_s\varphi }(0)$ in the semi-leptonic decay $D_s^{+}\to \varphi l^{+}{\nu }_l$. We have also included in our calculation the effect of the final state interaction ($fsi$) by working with the partial waves amplitudes $S$, $P$ and $D$. Numerical calculation shows that the decay amplitude is dominated by $S$ wave, and that the polarization is sensitive to the interference between $S$ and $D$ waves. The range of the phase difference ${\delta }_{SD}={\delta }_S-{\delta }_D$ accommodated by experimental error in $P_L$ is large.

Comments: 7 pages, LaTex